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Problem 57 Medium Difficulty

One in one hundred. That's the ratio of individuals in the U.S. population with autistic disorder, better known as autism. The disorder involves severe deficits in language, social bonding, and imagination, and is often accompanied by mental retardation. The bar graph shows the number of autism cases diagnosed in the United States from 2001 through 2008.
Autism Cases Diagnosed in the United States
CAN'T COPY THE GRAPH
Let $a_{n}$ represent the number of autism cases diagnosed in the United States, in thousands, $n$ years after 2000.
a. Use the numbers given in the graph to find and $$\text { interpret } \sum_{i=1}^{8} a_{i}$$
b. The finite sequence whose general term is $$a_{n}=28 n+63$$ where $n=1,2,3, \ldots, 8,$ models the number of autism cases diagnosed in the United States, in thousands, $n$ years after $2000 .$ Use this model to find $\sum_{i=1}^{8} a_{i} .$ Does this underestimate or overestimate the actual sum in part (a)? By how much?

Answer

a. $1515 ;$ A total of 1515 thousand, or $1,515,000,$ autism cases were diagnosed in the United States from 2001 through 2008 .
b. $1512 ;$ underestimates by 3 thousand

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Top Algebra Educators
Alayna H.

McMaster University

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Maria G.

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Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Video Transcript

so something our eyes someone to its We have 100 plus 1 20 plus 1 45 70 plus, our next term, that's, um, 200. And you have to 20. And then we have 2 16 and in 300 knowledge from all these together. Okay? And we get that information is equal to 1515 and these are the numbers of altruism cases.

University of California, Berkeley
Top Algebra Educators
Alayna H.

McMaster University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University